# Stored data for newform 105.4.i.e, downloaded from the LMFDB on 25 April 2024. {"label": "105.4.i.e", "space_label": "105.4.i", "level": 105, "weight": 4, "hecke_orbit": 5, "hecke_orbit_code": 18014948332404841, "dim": 10, "is_polredabs": true, "trace_hash": 1505968440393258362, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [7056, 13776, 26728, 5368, 5008, 352, 738, 26, 31, -1, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-3\\beta _{4}q^{3}+(\\beta _{1}-\\beta _{2}+\\beta _{3}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 1680, "analytic_conductor": 6.195200550602764, "hecke_ring_index": 28, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [105, 3, [71, 22, 31], [3, 3, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [16, 46], "field_disc": -4240152305983683145728, "field_disc_factorization": [[-1, 1], [2, 12], [3, 5], [7, 2], [9324157, 2]], "field_poly": [7056, 13776, 26728, 5368, 5008, 352, 738, 26, 31, -1, 1], "hecke_ring_index_factorization": [[2, 2], [7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.661", "prec": 17}, {"__RealLiteral__": 0, "data": "1.657", "prec": 17}, {"__RealLiteral__": 0, "data": "397.549", "prec": 24}, {"__RealLiteral__": 0, "data": "567.797", "prec": 24}, {"__RealLiteral__": 0, "data": "32443.485", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c3", "trace_display": [1, -15, 25, 56], "traces": [0, 10, 1, -15, -21, 25, -6, 56, -138, -45, -5, 33, -63, -46, -73, -150, -113, 136, 9, 39, -210, -147, -174, 133, 207, -125, 73, 270, -809, 544, -15, 430, 573, 99, -744, 35, 378, -3, 837, 69, -345, -1254, -372, 216, 1809, 225, -1637, 553, 678, -386, -50, 408, 1047, 1135, 27, 330, -1356, -234, 2564, 332, 315, 584, -3124, -63, 2274, -115, 261, -412, -1712, -798, -985, -284, 621, 2074, -605, -375, 18, -751, -438, -28, 565, -405, -1515, -1680, -1077, 1360, -40, -816, -4181, 2978, 90, -2736, 1062, 1290, 843, -195, 1719, -4336, -5183, -594, -525, 3216, 1116, 372, -6690, -840, 10838, 3986, -567, -2034, -435, 18, -5819, 3356, 2511, -665, -4192, 207, -2096, -3456, 2070, -4226, 4104, 1881, 1558, -1250, 1773, 142, 5509, -324, -365, 3453, -10854, -8835, 14064, 675, 12352, -1590, -4911, -688, -5840, -3318, 1254, 125, -1017, 1360, 1452, 1605, 10582, 832, 75, -654, 2817, -2448, -560, 4300, 3141, 6635, 5340, 3405, 5730, -1977, -162, 1280, -1069, -495, 8292, -7102, 2943, 2568, -1860, 351, -2860, -749, -15384, -1225, -27058, 996, 4834, 891, 945, 5336, 12031, -3504, -12577, 15, 4686, 5440, -1714, 1512, 8370, 5430, -3411, 3510, -12792, 690, -14193, -9674, 783, -4600, 1725, -1236, 11928, 11112, 10272, -3135, -2640, 1197, -11261, -7450, 1095, -31750, 15487, 426, -3534, 540, -3726, 5002, -5588, 6222, -9045, -6120, -1815, 21672, 16557, 2250, -4122, 600, -27, 10966, -16370, 13857, -14928, 4758, 657, -2765, -14884, 168, -36060, -3940, 1695, 9889, 10786, -1215, 18976, 745, 9090, -12893, -9346, 2520, -125, -1926, 10512, -15526, -3073, -2040, -3017, -4588, 240, -9249, 10470, -2448, -7281, 8448, -12543, 11350, 15889, -17868, -2836, -5852, -135, 8208, 39424, 12969, 34636, 825, -1593, -10382, -20944, -7740, -1875, -36738, 2529, 9210, -562, -585, 56426, 14092, -10314, -41323, -12820, 6504, 12178, -11922, -834, 3320, -1829, 891, -12800, 23089, 3150, 14732, 29684, 9648, -29677, -2920, 3348, 37216, 28035, -2232, -7810, -3180, 10035, 7464, 1806, 2205, 5784, -4222, -16257, -3960, 5685, -23916, -29905, -38832, -1701, 575, 17024, -6102, 70526, 28707, 2610, -8071, -19232, -27, 5273, -4120, 17868, -6176, -11868, -5034, 8560, -8938, -15066, 20468, 61680, -1995, -20159, -9214, -12576, -5432, -3100, -1242, -46237, 20728, 3144, -710, 380, 20520, -60674, -23148, -3105, -13014, -9372, 25356, -18709, 20740, 12312, -17481, 41653, 5643, -6050, 47007, -9348, -17922, -81912, 1875, -23141, -15232, -1971, 40034, 45, -213, 14338, 14673, -33054, 19340, 532, -972, 40880, 8878, -1095, -27168, -38970, -20718, -26013, 140, 16281, 15094, -3024, 8640, 5650, -3771, -21096, -3666, 21296, -4050, -9668, -48030, 37056, -8262, 7575, -4770, 21656, 23764, 29466, -4200, -19399, 1032, -31773, -10314, 12135, 35428, 6073, 4977, -40011, 3400, -7524, 4760, -94196, 375, 200, 1320, -3051, 31048, -4864, -8160, 13142, 37649, -2178, 12928, -41810, -1341, -584, 29216, -15873, -14890, -28612, -4992, 11276, 33174, 225, 15213, 11794, -1962, 54488, 7935, -16902, -9242, 11714, 3672, 2655, 4664, -1743, -63690, -40280, -6450, 43242, 4904, -18846, -7088, 8430, 19905, 40652, -15080, 16020, -1950, -32680, -20430, 31766, -3726, -8595, 24961, -58934, 8532, 143476, -10840, 243, -31012, 4320, -7680, -27305, -37992, -3207, 21392, -11147, -1485, 25468, -23208, -49752, -8900, 2625, 10653, -45211, 7656, 3375, 32160, 90129, -3852, -15791, -4622, 11160, -234, 52998, 1053, 21272, -1860, -8580, 72034, -1997, 4494, -16725, -783, 23076, 9634, -4186, -525, -59824, 37320, 40587, -28774, 27095, -5976, 18824, -90222, 14502, -19930, 7696, 2673, 77208, 36885, -5670, -24466, 50064, -8004, 27376, -20340, -29256, 5920, 46642, 5256, 2175, -39104, 75462, 4028, 104556, 45, 37048, -18619, 14058, -136728, 685, -32640, -9469, 46974, 2571, 8390, 103388, -3969, -142292, -32511, -12555, -43908, -26555, -32580, -97713, -6650, -10233, 7818, 8039, 10530, -41920, -5936, 76752, 945, -79118, -1035, -55061, 22348, -27999, 121828, -5240, 14511, 17, 41760, -4698, 16920, -27360, -13800, 62127, 15094, 5175, -59100, -93460, 7416, 49898, 21130, -17892, -747, -39602, -33480, 41040, 49429, -15408, -19355, -31468, 18810, -138165, -23256, -7920, 2911, -7790, 3591, -81232, 28742, 67566, -3125, 49868, 11175, -8661, -18512, 5580, -9604, 73848, 47625, -13422, 355, -92922, -44146, 74832, 1278, -27545, -24765, -10602, -49516, -30708, -3240, 64508, 1981, 5589, 105468, -3650, -18978, -1728, -17779, 8382, -17265, 57643, -37332, 1859, 23992, -27135, 10860, -74269, -18360, -156784, -29775, 10890, 56552, 68503, -32508, 35160, -11072, 40365, 22144, -69068, -3375, 47860, 10657, 24732, -49144, 123520, 1800, -8842, 1700, -81, -15900, -58501, -65796, 77392, -33533, 24555, -26256, -225414, -34812, 94004, -1720, 22392, 92560, -50348, -28548, -8975, 54044, 1971, 13825, -18607, -8295, -23096, -24992, 89304, -8916, -6270, -252, 3070, -62988, -10872, 1250, -34789, 5910, 15712, 30750, -10170, 60044, 126660, 29667, 29660, -6800, 32358, -16490, -43804, 7290, 3630, 91176, -28464, 61005, -64098, 5790, 3986, 38224, -13635, 15143, 26455, 77358, 172124, -118022, -28038, -4160, 30950, 7560, -117040, 25062, 750, 17458, 78649, 2889, -43684, -6540, -21843, 5988, -25155, 23289, -14085, -9907, 18438, -11438, 55092, -6120, -19429, -33108, -9051, -164802, -5705, 27528, 58382, -5597, -360, 10750, 167904, 40464, -117068, -9577, -15705, 31810, 27032, 14688, 24139, 66350, -21843, -94790, -14483, 25344, 53400, -33408, 75258, 37304, -116594, -17025, -60736, 86300, -7215, 37472, 14325, 26802, 26615, -61974, 17016, 4335, 90276, -17556, -61456, 66511, -405, 93666, -128792, -49248, 46145, -6400, -59136, 40812, 236132, -14283, -10690, -58466, -51954, 22352, 3496, -4950, -21852, -134244, -4779, -59388, -41460, -31146, 9818, -28808, 125664, -17755, 28253, 11610, -22921, 151040, 20340, 33006, -5206, 55107, 73435, 6420, -15174, -6502, -186830, 27630, 9300, -75365, -1686, -50098, 70512, 3510, -8242, 80246, -84639, -75124, -28600, 15321, -175008, -59231, 15471, 3745, 52856, 247938, 89410, -24080, -38460, 30140, -33450, 19512, -31982, -7000, -73068, -7885, 7976, 17883, -67645, 8694, 49149, 41188, -145496, -4980, 20664, 25868, 10974, -10896, 48340, 2673, -54420, 71813, -38400, 8910, 70487, -138534, 156575, -73032, -4725, 57232, -373438, -61608, -39964, 13340, -44526, 14174, -47552, -57888, 11395, -19812, -89031, -1944, -159466, -8760, -3180, -205745, -20088, 61568, 62885, -55824, -53688, 214996, -184716, 150, -110109, 3348, 114936, 19357, 46860, 148767, 247508, -9540, 29928, -27200, 30105, 127456, 102084, -44784, -4285, -71382, -2709, -152407, 364248, 945, -417512, 111322, -8676, 63994, 20925, 25332, 359360, -140520, -48771, -27150, -18030, -11880, 42548, 163682, -34110, 4131, 87803, 35874, 31161, 35100, -92685, -66208, 5814, 58248, 63960, -43235, 10206, -86076, -256176, 1725, -47616, 103514, 51072, 28308, -117630, 36612, -31836, -108261, -105789, -24185, -91296, -18396, -35398, -113488, -3915, -52426, -21138, 48426, 202442, -46000, -57696, -111994, 48468, -81, 17250], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "105.4.i.e", "char_is_minimal": true, "conrey_index": 16, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 0, 0, 0, 0, 0], [0, 1, -1, 1, -4, 0, 0, 0, 1, 0], [5, 0, 0, 0, -5, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [7, 1, 1, 0, -3, 0, 1, 0, 0, 1], [-12, 1, -1, 5, 0, 2, 0, -1, 0, 1], [-9, 0, 0, 0, 9, 0, 0, 0, 0, 0], [0, 5, 0, 5, 0, 0, 0, 0, 0, 0], [0, 1, 4, 2, 6, -1, 2, 0, -4, 1], [-12, -3, 0, 0, 12, 0, 0, 0, -3, 0], [-7, -2, -3, -4, 0, -3, 1, 2, 0, -2], [0, 14, -1, 3, -18, -3, -1, 2, 0, -1], [-15, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-16, -18, 0, 3, 16, 1, 3, -4, -3, 5], [0, 6, -3, 4, 30, 2, 1, 5, 3, 3], [0, -9, 0, -9, 0, 0, 0, 0, 0, 0], [13, -16, 0, 2, -13, -2, 2, 0, 2, 6], [-20, 0, -5, 5, 0, 0, 0, 0, 0, 0], [-9, 0, -3, 3, -12, 0, 0, 0, 3, -3], [-30, -6, 1, -39, 0, -12, 0, 6, 0, -6], [18, 28, 0, -3, -18, -2, -3, 5, -8, -4], [0, -15, 3, -12, 36, -3, 3, -3, -3, 0], [0, 0, 0, 0, -25, 0, 0, 0, 0, 0], [18, -22, 0, -1, -18, 1, -1, 0, 12, -3], [27, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24, 10, -11, 26, -100, 3, -3, -2, 15, 3], [48, 2, 1, -40, 0, 5, 1, -2, 0, 2], [0, -15, 0, 0, 0, 0, 0, 0, 0, 0], [0, 29, 3, 30, 91, -1, -3, -5, -3, -4], [0, -29, 23, -28, 108, -1, 3, 1, -23, 2], [18, -6, 0, -3, -18, 0, -3, 3, 12, -6], [-66, 7, -30, 14, 0, 4, -10, -7, 0, 7], [20, 5, 0, 5, -35, 0, 5, 0, 5, 0], [36, 0, 9, -9, 0, 0, 0, 0, 0, 0], [-5, 12, 0, -2, 5, -3, -2, 5, -15, -1], [0, 11, 14, 13, 168, -2, -2, -6, -14, -4], [0, 12, 9, 6, 21, 6, -9, 3, -9, -3], [-60, -20, 0, 5, 60, 5, 5, -10, -5, 5], [-114, 7, 16, 29, 0, 19, 5, -7, 0, 7], [-54, -9, 3, 33, 54, 6, 0, 3, -3, 3], [35, 13, 10, 15, 0, 23, -3, -13, 0, 13], [348, 44, 0, -5, -348, -1, -5, 6, 43, -9], [0, 0, 0, 0, 45, 0, 0, 0, 0, 0], [0, -5, -45, -3, -330, -2, -2, -6, 45, -4], [102, -12, 0, -11, -102, -1, -11, 12, -3, -21], [48, -9, 9, -63, 0, -12, 6, 9, 0, -9], [-68, 60, 30, 33, 57, -1, -1, -4, -3, -5], [0, 0, 0, 25, 0, 0, 0, 0, 0, 0], [90, -12, 0, 6, -90, 15, 6, -21, -9, -3], [0, 61, -1, 63, 220, -2, 12, 8, 1, 10], [0, -75, 11, -80, 216, 5, -13, -3, -11, -8], [0, 27, 0, 0, 0, 0, 0, 0, 0, 0], [30, -5, 20, 5, 0, -5, 5, 5, 0, -5], [-120, 25, -19, 143, 36, 16, 0, -27, -16, 9], [-39, -6, -6, -54, 0, 0, 12, 6, 0, -6], [498, 89, 0, 3, -498, -3, 3, 0, 24, 9], [0, 32, -33, 18, 84, 14, -31, -3, 33, -17], [0, -15, 15, -15, 60, 0, 0, 0, -15, 0], [124, -66, 0, -6, -124, -4, -6, 10, -18, -8], [-336, -5, -7, -98, 0, 0, 10, 5, 0, -5], [-36, -9, 0, -9, 63, 0, -9, 0, -9, 0], [196, -1, 3, -153, 0, -20, -18, 1, 0, -1], [-35, 10, 0, -10, 35, -5, -10, 15, -15, -15], [0, 117, -3, 99, 90, 18, -18, 18, 3, 0], [0, -127, -20, -128, -107, 1, 12, 14, 20, 13], [-264, -252, 0, 28, 264, 10, 28, -38, 8, 46], [-54, 9, 24, 93, 0, 15, -3, -9, 0, 9], [-90, 55, 0, 70, 0, -5, -5, 15, -5, 0], [-54, -22, -9, -40, 0, -45, -1, 22, 0, -22], [108, 36, 0, -9, -108, -9, -9, 18, 9, -9], [0, -21, 2, -4, 397, -17, 22, -12, -2, 5], [0, -101, -30, -90, -150, -11, 5, -17, 30, -6], [-75, 0, 0, 0, 75, 0, 0, 0, 0, 0], [-28, -2, 33, -141, 0, -24, -20, 2, 0, -2], [-384, 9, 60, -10, 576, -30, 6, 27, -47, -24], [-54, 3, -36, -63, 0, 0, -6, -3, 0, 3], [31, -88, 0, 19, -31, 17, 19, -36, 15, 21], [0, -105, 15, -90, 80, -15, 25, -5, -15, 10], [0, 0, 0, 0, -81, 0, 0, 0, 0, 0], [-294, -55, 0, -2, 294, -26, -2, 28, -91, 22], [-192, 0, 25, -120, 0, -27, -27, 0, 0, 0], [-300, -78, -12, -48, 372, -6, 18, -3, -33, 9], [150, 10, -15, 30, 0, 35, 15, -10, 0, 10], [-6, 70, 0, 16, 6, -4, 16, -12, -81, 36], [0, 120, -3, 126, -144, -6, 3, -9, 3, -3], [0, 441, -55, 436, -744, 5, -7, 3, 55, -2], [612, -82, 0, 0, -612, 9, 0, -9, -13, -9], [0, 0, 0, -45, 0, 0, 0, 0, 0, 0], [-487, -103, -55, -142, 375, -27, 7, 25, 69, 8], [204, 17, -31, 421, 0, 54, 20, -17, 0, 17], [273, -90, 0, -3, -273, -15, -3, 18, 9, 9], [0, 101, -25, 82, 204, 19, -21, 17, 25, -2], [0, -90, -10, -80, -65, -10, 30, 10, 10, 20], [324, 84, 0, -3, -324, 3, -3, 0, 69, -9], [-424, -26, -42, 152, 0, -10, 42, 26, 0, -26], [-396, 143, -39, -61, -324, -31, -19, 65, 27, -32], [-54, 9, -36, -9, 0, 9, -9, -9, 0, 9], [-100, -25, 0, 0, 100, 0, 0, 0, -25, 0]]}